A father (m= 90 kg) and son (m= 45 kg) are standing facing each other on a frozen pond. The son pushes on the father and finds himself moving backward at 3 after they have separated. How fast is the father moving?
To determine the speed at which the father is moving, use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum before an event is equal to the total momentum after the event, as long as no external forces act on the system.
In this scenario, we have a system consisting of the father and the son. Initially, they are at rest, so their total momentum is zero. After the son pushes the father, the father starts moving and the son moves backward. Let's say the speed at which the son moves backward is v (in m/s).
The momentum of an object can be calculated by multiplying its mass by its velocity. Since the father and son move in opposite directions, we consider their velocities as positive and negative values. So, we have:
Initial momentum of the system (before push) = 0
Final momentum of the system (after push) = momentum of the father + momentum of the son
The momentum of an object is given by the equation: momentum = mass * velocity.
For the father:
Final momentum of the father = mass of the father * velocity of the father
= 90 kg * v m/s
= 90v kg·m/s
For the son:
Final momentum of the son = mass of the son * velocity of the son
= 45 kg * (-3 m/s)
= -135 kg·m/s
According to the principle of conservation of momentum, the final momentum should be equal to the initial momentum:
0 = 90v kg·m/s - 135 kg·m/s
Simplifying the equation:
135 kg·m/s = 90v kg·m/s
Dividing both sides of the equation by 90 kg·m/s, we get:
1.5 m/s = v
Therefore, the father is moving at a speed of 1.5 m/s.